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Relaxing monotonicity in the identification of local average treatment effects

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  • Huber, Martin

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  • Mellace, Giovanni

    ()

Abstract

In heterogeneous treatment effect models with endogeneity, the identification of the local average treatment effect (LATE) typically relies on an instrument that satisfies two conditions: (i) joint independence of the potential post-instrument variables and the instrument and (ii) monotonicity of the treatment in the instrument, see Imbens and Angrist (1994). We show that identification is still feasible when replacing monotonicity by a strictly weaker local monotonicity condition. We demonstrate that the latter allows identifying the LATEs on the (i) compliers (whose treatment reacts to the instrument in the intended way), (ii) defiers (who react counter-intuitively), and (iii) both populations jointly. Furthermore, (i) and (iii) coincides with standard LATE if monotonicity holds. We also present an application to the quarter of birth instrument of Angrist and Krueger (1991).

Suggested Citation

  • Huber, Martin & Mellace, Giovanni, 2012. "Relaxing monotonicity in the identification of local average treatment effects," Economics Working Paper Series 1212, University of St. Gallen, School of Economics and Political Science.
  • Handle: RePEc:usg:econwp:2012:12
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    File URL: http://ux-tauri.unisg.ch/RePEc/usg/econwp/EWP-1212.pdf
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    References listed on IDEAS

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    1. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-323, May.
    2. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
    3. Alberto Abadie & Joshua Angrist & Guido Imbens, 2002. "Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings," Econometrica, Econometric Society, vol. 70(1), pages 91-117, January.
    4. Rashmi Barua & Kevin Lang, 2009. "School Entry, Educational Attainment and Quarter of Birth: A Cautionary Tale of LATE," NBER Working Papers 15236, National Bureau of Economic Research, Inc.
    5. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, September.
    6. JAMES G. MacKINNON, 2006. "Bootstrap Methods in Econometrics," The Economic Record, The Economic Society of Australia, vol. 82(s1), pages 2-18, September.
    7. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June.
    8. Frolich, Markus, 2007. "Nonparametric IV estimation of local average treatment effects with covariates," Journal of Econometrics, Elsevier, vol. 139(1), pages 35-75, July.
    9. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    10. Dai, J. & Sperlich, S., 2010. "Simple and effective boundary correction for kernel densities and regression with an application to the world income and Engel curve estimation," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2487-2497, November.
    11. Klein, Tobias J., 2010. "Heterogeneous treatment effects: Instrumental variables without monotonicity?," Journal of Econometrics, Elsevier, vol. 155(2), pages 99-116, April.
    12. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    13. Martin Huber & Giovanni Mellace, 2010. "Sharp IV bounds on average treatment effects under endogeneity and noncompliance," University of St. Gallen Department of Economics working paper series 2010 2010-31, Department of Economics, University of St. Gallen.
    14. Card, David, 1999. "The causal effect of education on earnings," Handbook of Labor Economics,in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 30, pages 1801-1863 Elsevier.
    15. Toru Kitagawa, 2009. "Identification region of the potential outcome distributions under instrument independence," CeMMAP working papers CWP30/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    16. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, January.
    17. Joshua D. Angrist & Alan B. Keueger, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, Oxford University Press, vol. 106(4), pages 979-1014.
    18. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355.
    19. A. D. Roy, 1951. "Some Thoughts On The Distribution Of Earnings," Oxford Economic Papers, Oxford University Press, vol. 3(2), pages 135-146.
    20. Guido W. Imbens & Donald B. Rubin, 1997. "Estimating Outcome Distributions for Compliers in Instrumental Variables Models," Review of Economic Studies, Oxford University Press, vol. 64(4), pages 555-574.
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    Citations

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    Cited by:

    1. Will Dobbie & Jae Song, 2015. "Debt Relief and Debtor Outcomes: Measuring the Effects of Consumer Bankruptcy Protection," American Economic Review, American Economic Association, vol. 105(3), pages 1272-1311, March.
    2. Clément de Chaisemartin, 2012. "Late again, whithout Monotonicity," Working Papers 2012-12, Center for Research in Economics and Statistics.
    3. Clément De Chaisemartin & Xavier D'Haultfoeuille, 2012. "Late Again with Defiers," PSE Working Papers halshs-00699646, HAL.
    4. de Chaisemartin, Clement, 2013. "Defying the LATE? Identification of local treatment effects when the instrument violates monotonicity," The Warwick Economics Research Paper Series (TWERPS) 1020, University of Warwick, Department of Economics.
    5. Clément De Chaisemartin & Xavier D'Haultfoeuille, 2012. "Late Again with Defiers," Working Papers halshs-00699646, HAL.
    6. Fiorini, Mario & Katrien Stevens, 2014. "Assessing the Monotonicity Assumption in IV and fuzzy RD designs," Working Papers 2014-13, University of Sydney, School of Economics.

    More about this item

    Keywords

    Instrumental variable; treatment effects; LATE; local monotonicity;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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